(Circle the correct response) The purpose of the F Test in simple linear regress
ID: 3220864 • Letter: #
Question
(Circle the correct response) The purpose of the F Test in simple linear regression is to test for a. independence of variables b. statistical significance of the dependent variable c. multicollinearity d. statistical significance of the linear model True or False: The purpose of the coefficient of determination, R^2, is to give a numerical measure of the typical amount of error in using the estimation equation. (Circle the correct response) The purpose of the t test in simple linear regression is to test for a. independence of variables b. statistical significance of the independent variable c. multicollinearity d. statistical significance of correlation coefficients (Circle the correct response) A linear regression analysis between demand for a product, y (in number of units) and the price of the unit, x (in $1,000s) resulted in the estimated regression equation y vector = 1400-25x. An increase of $3,000 in unit price will result in what impact on demand in numbers of units? a. An increase of 75,000 units b. An increase of 1, 325 units c. A decrease of 75,000 units d. A decrease of 75 units Circle all of the following which are true. A. SSR = SST + SSE b. SSR + SSE = 1 c. 0 lessthanorequalto SSR/SST lessthanorequalto 1 d. (SSR/SST) + (SSE/SST) = 1Explanation / Answer
7. The F-test in linear regression is used to test for statistical significance of the linear model. So option (D) is correct.
Since F-statistic is given by F = MSReg / MSRes.
8. R^2 = SSReg / SST = 1 - (SSRes / SST). So more the SSRes, lesser the R^2. So R^2 gives a kind of numerical measure of the amount of error.
Hence the statement is true.
9. The t-test in simple linear regression is used to test statistical significance of the independent variables.
So option (B) is correct.
10. Let y1 = 1400 - 25 * x1
and y2 = 1400 - 25 * (x1 + 3) = 1400 - 25 * x1 - 75 ( As x1 is in $1000)
Hence, y2 - y1 = -75
Hence there will be a decrease of 75 units.
So option (D) is correct.
11. We know, SST= SSR +SSE. Hence, 0 <= SSR/SST <= 1.
Also, (SSR/SST) + (SSE/SST) = SST/SST = 1.
So option (C) and option (D) are true.
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